Believe in yourself.

Question, “What must I do to have a long and prosperous art career?”
To have long career in the Art Business you will need to concentrate on a few things.
Firstly if you are painting to make your fortune, you picked the wrong profession, become a lawyer. 
I believe most serious dedicated Artists can make a very good living from their Art, but will all their paintings end up in the auctions and great museums, very few will sadly.
The love of painting and the need to paint must be your only driving force. 
Your belief in your own ability must be resolute.
Do not look for reassurance from others, everyone has their own agenda, you are painting because you are confident of your own talent and ability and what others think is not important. 
What if Monet had listened to to the Art Market and his friends and family, we would have no beautiful Impressionist paintings today.
You must bring your change, New Art, original Art and that can only happen if you believe in yourself, do not listen to the noise.
You have to be a trail blazer, make your own map as you go forward, do not follow the path of the well trodden.
The reality is that it is a hard business, but if you concentrate on your love of painting and make that the great motivation of your career, then the rest will fall into place.
Picasso only heard one voice, his own, because he knew he was Picasso, so tune out all the other voices and only hear yours.
Validate your painting by the act of painting and you will bring change, to your own career and to your Art world.
Believe in yourself resolutely.